zero moment point
In plain wordsThe spot on the ground beneath a walking robot where the floor's push balances out; keeping it inside the area under the robot's feet stops the robot from tipping over.
A point on the ground used to judge whether a walking robot will tip: the spot where the moments of the ground's reaction forces on the feet, taken about horizontal axes, cancel out, which is also where the combined pull of gravity and the robot's own accelerations meets the floor. While the zero moment point stays strictly inside the support polygon (the convex hull of the feet's contact areas), the feet do not roll over their edges and the robot does not tip; as it reaches the boundary, the robot begins to topple. ZMP-based walking plans center-of-mass trajectories, often with a linear inverted-pendulum model and preview control, so that the ZMP follows a safe reference, then tracks it with feedback from force sensors in the feet. The criterion underpinned Honda's humanoids and most bipeds from the 1990s to the 2010s, but it presumes feet resting flat on ground that will not let them slip, and it tends to produce cautious, flat-footed gaits; learned controllers and whole-body model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements. now often replace it.
The ZMP drifted toward the toe edge, so the controller shortened the next step.
Origin
Introduced by Miomir Vukobratović and Davor Juričić in January 1968 at the Third All-Union Congress of Theoretical and Applied Mechanics in Moscow; the name 'zero moment point' was established in Vukobratović's papers of 1970–1972.
Usage note
Often equated with the center of pressure; the two coincide while the robot is balanced, but the ZMP is defined from the robot's dynamics, whereas the center of pressure is measured from contact forces.
Related
- legged robotlegged robot, n.: A robot that walks on legs instead of rolling on wheels, such as a four-legged 'robot dog' or a two-legged humanoid, so it can climb stairs and cross rough ground.
- humanoid robothumanoid robot, n.: A robot built roughly in human shape, with a head, torso, two arms and usually two legs, so that it can work in spaces and with tools designed for people.
- locomotionlocomotion, n.: How a robot moves itself from place to place: rolling on wheels, walking on legs, crawling, swimming or flying.
- model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.
- control theorycontrol theory, n.: The mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does.
Sources
- Vukobratović, M. & Borovac, B. (2004). Zero-moment point — thirty five years of its life. International Journal of Humanoid Robotics 1(1), 157–173.
Mentioned in
humanoid robothumanoid robot, n.: A robot built roughly in human shape, with a head, torso, two arms and usually two legs, so that it can work in spaces and with tools designed for people., legged robotlegged robot, n.: A robot that walks on legs instead of rolling on wheels, such as a four-legged 'robot dog' or a two-legged humanoid, so it can climb stairs and cross rough ground., locomotionlocomotion, n.: How a robot moves itself from place to place: rolling on wheels, walking on legs, crawling, swimming or flying.